Mobile companies certainly can, but not necessarily so, do what @patrakov says.
But most companies do add OS extensions that inform them when hotspot/tethering is turned on.
I think it is country-dependent. In countries where carrier-locked phones are the norm, perhaps @bluewavenet is right. But for Russia, the predominant technique is based on the TTL.
If you use a supported openwrt router with an usb or internal modem (cell phone via usb should work just fine BUT NOT via WIFI as it counts as tethering) you can easily bypass any ttl checks that your isp employs.
There are as well methods for rooted phone but that's outside the scope of this forum.